Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l }
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \
F ( x ) = 3 x ^ { 2 } - 6
\end{array}$$
A) $F ( x ) = ( f \circ g ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
D) $F ( x ) = ( g \circ f ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \
F ( x ) = 3 x ^ { 2 } - 6
\end{array}$$
A) $F ( x ) = ( f \circ g ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
D) $F ( x ) = ( g \circ f ) ( x )$

Quizplus · Accepted Answer

F(x) can be rewritten as 3(x^2 - 2), which is g(f(x)) because f(x) = x^2 - 2 and g(x) = 3x.

Write the Function F(x) as a Composition of F, G f(x)=x2−2g(x)=3xh(x)=x−8F(x)=3x2−6\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \\F ( x ) = 3 x ^ { 2 } - 6\end{array}f(x)=x2−2g(x)=3xh(x)=x−8​F(x)=3x2−6​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \\F ( x ) = 3 x ^ { 2 } - 6\end{array}$